We demonstrate first measurements of successful spin generation in crystalline ${\mathrm{Co}}_{2}\mathrm{FeSi}$/MgO/GaAs hybrid structures grown by molecular-beam epitaxy (MBE) with different MgO interlayer thicknesses. Using nonlocal spin valve and nonlocal Hanle measurement configurations, we determine spin lifetimes of $\ensuremath{\tau}\ensuremath{\approx}100$ ns and spin diffusion lengths of $\ensuremath{\lambda}\ensuremath{\approx}5.6\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{m}$ for different MgO layer thicknesses, proving the high quality of the GaAs transport channel. For an optimized MgO layer thickness, the bias dependence of the spin valve signals indicates the verification of the half-metallic gap (upper edge) of ${\mathrm{Co}}_{2}\mathrm{FeSi}$ in accordance with first-principles calculations. In addition to that, spin generation efficiencies of up to $18%$ reveal the high potential of MgO interlayers at the ${\mathrm{Co}}_{2}\mathrm{FeSi}$/GaAs interface for further device applications.
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